The discussion about energy options tends to be an intensely emotional, polarised, mistrustful, and destructive one. Every option is strongly opposed: the public seem to be anti-wind, anti-coal, anti-waste-to-energy, anti-tidal-barrages, anti-carbon-tax, and anti-nuclear.

We can't be anti-everything – we need an energy plan that adds up. But there's a lack of numeracy in the public discussion of energy. Where people do use numbers, they select them to sound big and score points in arguments, rather than to aid thoughtful discussion.

I think it highlights the scale of the problem if we discuss all forms of energy in simple personal units. In my book, Sustainable Energy – without the hot air, I express everything in kilowatt-hours. One kilowatt-hour (kWh) is the electrical energy used by leaving a 40-watt bulb on for 24 hours. The chemical energy in the food we eat to stay alive amounts to about three kWh per day. Taking one hot bath uses about five kWh of heat. Driving an average car 50km uses 40 kWh of fuel.

With a few of these numbers in mind, we can start to evaluate some of the recommendations people make about energy.

Take, for example, switching off your mobile phone charger when you are not using it. The truth is that leaving a phone charger switched on uses about 0.01 kWh per day – one hundredth of the power consumed by a lightbulb and the same as driving an average car for one second. Switching off phone chargers is like bailing the Titanic with a teaspoon. I'm not saying you shouldn't switch it off – do switch if off – but realise what a tiny fraction it is of your energy footprint.

In total, the European lifestyle uses 125 kWh per day per person for transport, heating, manufacturing, and electricity. That's equivalent to every person having 125 lightbulbs switched on all the time.

And most of this energy today comes from fossil fuels. What are our post-fossil-fuel options?

Among the energy-saving options, two technology switches look particularly promising. Electric vehicles will help because they can be about four times as energy-efficient as standard fossil-fuel vehicles. There is also the delivery of winter heating and hot water by electric-powered heat pumps (which can be four times as energy-efficient as standard heaters).

Now let's imagine that technology switches and lifestyle changes manage to halve British energy consumption to 60kWh per day per person. How big would the wind, nuclear, and solar facilities need to be to supply this halved consumption?

If we wanted to get one-third of our energy from each of these sources we would have to build wind farms with an area equal to the area of Wales, 50 Sizewells of nuclear power and solar power stations in deserts covering an area twice the size of greater London.

I'm not recommending this particular mix of options – there are many mixes that add up. What about tidal power, wave, geothermal, biofuels and hydroelectricity? In such a short article, I can't discuss all the technology options. But the sober message about wind and solar applies to all renewables: much as I love them, they only deliver a small amounts of power. So if we want renewable facilities to supply power on a scale comparable to our consumption, those facilities – whether centralised or decentralised – must be big.

Whatever mix you choose, if it adds up, we have a very large building task. The simple wind/nuclear/solar mix I just mentioned would involve roughly a one-hundred-fold increase in wind power, and a five-fold increase in nuclear power; the solar power in deserts would require new long-distance cables connecting the Sahara to Surrey, with a capacity 25 times greater than the existing England-France interconnector.

It's not going to be easy to make a energy plan that adds up; but it is possible. We need to get building.

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• David MacKay is a professor in the Department of Physics at the University of Cambridge. His book, Sustainable Energy – Without the Hot Air, is published by UIT Cambridge, and is also available in electronic form for free from www.withouthotair.com